Homotopy Analysis Method for Variable Thermal Conductivity Heat Flux Gage with Edge Contact Resistance

2010 ◽  
Vol 65 (10) ◽  
pp. 771-776 ◽  
Author(s):  
Abdul Aziz ◽  
Farzad Khani ◽  
Mohammad Taghi Darvishi
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Contact Resistance ◽  
Homotopy Analysis Method ◽  
Heat Sink ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Radiation Emission ◽  
Homotopy Analysis

The homotopy analysis method (HAM) has been used to develop an analytical solution for the thermal performance of a circular-thin-foil heat flux gage with temperature dependent thermal conductivity and thermal contact resistance between the edge of the foil and the heat sink. Temperature distributions in the foil are presented illustrating the effect of incident heat flux, radiation emission from the foil, variable thermal conductivity, and contact resistance between the foil and the heat sink. The HAM results agree up to four places of decimal with the numerical solutions generated using the symbolic algebra package Maple. This close comparison vouches for the high accuracy and stability of the analytic solution.

APPLICATION OF THE NEW SPECTRAL HOMOTOPY ANALYSIS METHOD (SHAM) IN THE NON-LINEAR HEAT CONDUCTION AND CONVECTIVE FIN PROBLEM WITH VARIABLE THERMAL CONDUCTIVITY

2012 ◽  
Vol 09 (03) ◽  
pp. 1250039 ◽  
Author(s):  
S. S. MOTSA
Keyword(s):  
Thermal Conductivity ◽  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Linear Heat ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Convective Fin ◽  
Spectral Homotopy Analysis Method

In this work, we demonstrate the efficiency of the newly developed spectral homotopy analysis method (SHAM) in solving non-linear heat transfer equations. We demonstrate the applicability of the method by solving the problem of steady conduction in a slab and the convective fin equation with variable thermal conductivity. New closed form explicit analytic solutions of the governing non-linear equations are obtained and compared with the SHAM results and numerical solutions. The results reveal that the new SHAM approach is very accurate and efficient and converges much faster than the standard homotopy analysis method.

Radiative Flow with Variable Thermal Conductivity in Porous Medium

2012 ◽  
Vol 67 (3-4) ◽  
pp. 153-159 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Muhammad Qasim ◽  
A. Alsaedi
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Differential Equations ◽  
Radiation Effect ◽  
Numerical Solutions ◽  
Variable Thermal Conductivity ◽  
Analysis Method ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Homotopy Analysis

This article considers the radiation effect on the flow of a Jeffery fluid with variable thermal conductivity. Similarity transformations are employed to convert the partial differential equations into ordinary differential equations. The resulting equations have been computed by the homotopy analysis method (HAM). The numerical values of the local Nusselt numbers are also computed. The comparison with the numerical solutions of qƟ'(0) is presented. The obtained results are displayed and physical aspects have been examined in detail

Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

2010 ◽  
Vol 65 (11) ◽  
pp. 935-949 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian ◽  
Abbas Saadatmandi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Analysis Method ◽  
Partial Differential ◽  
Integer Order ◽  
Homotopy Analysis

In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

scholarly journals Application of the Homotopy Method for Fractional Inverse Stefan Problem

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5474
Author(s):  
Damian Słota ◽  
Agata Chmielowska ◽  
Rafał Brociek ◽  
Marcin Szczygieł
Keyword(s):  
Heat Flux ◽  
Approximate Solution ◽  
Temperature Distribution ◽  
Continuous Function ◽  
Homotopy Analysis Method ◽  
Input Data ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The One

The paper presents an application of the homotopy analysis method for solving the one-phase fractional inverse Stefan design problem. The problem was to determine the temperature distribution in the domain and functions describing the temperature and the heat flux on one of the considered area boundaries. It was demonstrated that if the series constructed for the method is convergent then its sum is a solution of the considered equation. The sufficient condition of this convergence was also presented as well as the error of the approximate solution estimation. The paper also includes the example presenting the application of the described method. The obtained results show the usefulness of the proposed method. The method is stable for the input data disturbances and converges quickly. The big advantage of this method is the fact that it does not require discretization of the area and the solution is a continuous function.

scholarly journals Numerical Solutions of Heat Transfer for Magnetohydrodynamic Jeffery-Hamel Flow Using Spectral Homotopy Analysis Method

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 626 ◽  
Author(s):  
Asad Mahmood ◽  
Md Md Basir ◽  
Umair Ali ◽  
Mohd Mohd Kasihmuddin ◽  
Mohd. Mansor
Keyword(s):  
Heat Transfer ◽  
Temperature Profile ◽  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Reynold Number ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear Differential ◽  
Spectral Homotopy Analysis Method

This paper studies heat transfer in a two-dimensional magnetohydrodynamic viscous incompressible flow in convergent/divergent channels. The temperature profile was obtained numerically for both cases of convergent/divergent channels. It was found that the temperature profile increases with an increase in Reynold number, Prandtl number, Nusselt number and angle of the wall but decreases with an increase in Hartmann number. A relatively new numerical method called the spectral homotopy analysis method (SHAM) was used to solve the governing non-linear differential equations. The SHAM 3rd order results matched with the DTM and shooting, showing that SHAM is feasible as a technique to be used.

Modified Homotopy Analysis Method for Nonlinear Aeroelastic Behavior of Two Degree-of-Freedom Airfoils

2016 ◽  
Vol 16 (09) ◽  
pp. 1520001 ◽  
Author(s):  
Yaobin Niu ◽  
Zhongwei Wang ◽  
Dequan Wang ◽  
Bing Liu
Keyword(s):  
Homotopy Analysis Method ◽  
Control Parameter ◽  
Numerical Solutions ◽  
Degree Of Freedom ◽  
Aerodynamic Load ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Two Degree Of Freedom ◽  
Convergence Control Parameter

In this paper, the homotopy analysis method (HAM) is extended to deal with the nonlinear aeroelastic problem of a two degree-of-freedom (DOF) airfoil. To avoid determination of the parameter for the complicated high-order minimization problem, a new modified HAM is proposed based on the idea of minimizing the squared residual. Using this method, the convergence-control parameter is determined by the low order squared residual of the governing equations, and then the problem is solved in a way similar to the basic HAM. The proposed method is used to solve the nonlinear aeroelastic behavior of a supersonic airfoil, with the unsteady aerodynamic load evaluated by the piston theory. Two examples are prepared, for which the frequencies and amplitudes of the limit cycles are obtained. The approximate solutions obtained are demonstrated to agree excellently the numerical solutions, meanwhile, the convergence-control parameter can be easily determined using the present approach.

scholarly journals The Approximate Solutions of Fredholm Integrodifferential-Difference Equations with Variable Coefficients via Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Seydi Battal Gazi Karakoç ◽  
Aytekin Eryılmaz ◽  
Musa Başbük
Keyword(s):  
Difference Equations ◽  
Homotopy Analysis Method ◽  
Algebraic System ◽  
Numerical Solutions ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

Numerical solutions of linear and nonlinear integrodifferential-difference equations are presented using homotopy analysis method. The aim of the paper is to present an efficient numerical procedure for solving linear and nonlinear integrodifferential-difference equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system.

The Application of Homotopy Analysis Method to Determine the Thermal Response of Convective-Radiative Porous Fins with Temperature-Dependent Properties

2019 ◽  
Vol 11 (09) ◽  
pp. 1950089 ◽  
Author(s):  
Omid Zargar ◽  
Masoud Mollaghaee-Roozbahani ◽  
Mohammad Bashirpour ◽  
Mostafa Baghani
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Homotopy Analysis Method ◽  
Internal Heat ◽  
Thermal Response ◽  
Heat Transfer Analysis ◽  
Analysis Method ◽  
Temperature Dependent ◽  
Porous Fin ◽  
Homotopy Analysis

In this paper, the Homotopy Analysis Method (HAM) is utilized to investigate the thermal response of a circular convective-radiative porous fin having a rectangular cross-section. It is assumed that internal heat generation depends linearly on the temperature for the solid part of the porous fin, while temperature-dependent functions are used for thermal conductivity and convective terms. The thermal conductivity and convective coefficient of heat transfer are supposed to change respectively as a nonlinear hyperbolic and as a power-law function of the temperature all through the fin length. The function employed for the thermal conductivity can be applied for the thermal analysis if for example fins are made of semiconductor materials. Additionally, the general form of convective function enables us to account for the convection heat transfer in different processes. The heat transfer analysis in the porous media is conducted through passage velocity in Darcy’s model. HAM is utilized to study the effects of different pertinent parameters and nondimensional numbers on the described problem. The accuracy and convergence of HAM are validated with numerical methods (i.e., Runge–Kutta method) as well as other published works that reveal an excellent agreement.

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